GQ and Schnorr Identification Schemes: Proofs of
Security against Impersonation under Active and Concurrent Attacks

Authors: M. Bellare and A. Palacio

Abstract: The Guillou-Quisquater (GQ) and Schnorr identification
schemes are amongst the most efficient and best-known Fiat-Shamir follow-ons,
but the question of whether they can be proven secure against impersonation
under active attack has remained open. This paper provides such a proof for GQ
based on the assumed security of RSA under one more inversion, an extension of
the usual one-wayness assumption that was introduced by Bellare, Namprempre,
Pointcheval and Semanko. It also provides such a proof for the Schnorr scheme
based on a corresponding discrete-log related assumption. These are the first
security proofs for these schemes under assumptions related to the underlying
one-way functions. Both results extend to establish security against
impersonation under concurrent attack.